LionTree, powered by what media and telecom executives describe as Mr. Bourkoff’s nonstop networking, has already claimed a number of advisory assignments, from Charter’s deal for Time Warner Cable to Verizon’s purchases of AOL and Yahoo to helping advise Snap Inc. on its initial public offering. Over all, the firm has advised on more than $350 billion worth of transactions.

“Aryeh is going to be involved or peripherally involved in everything that’s going on,” said Les Moonves, the chief of CBS.

Mr. Bourkoff said he was ready to turn the moment to his advantage.

“It’s a fortunate thing that we happen to be at the right place at the right time,” Mr. Bourkoff said in an interview in his Midtown Manhattan office. He added, “The entire firm today, based on what we see coming into the future, is keenly structured to play into that.”

Standing out among independent investment banks, many started in the wake of the 2008 financial crisis, is difficult. Mr. Bourkoff and his team at LionTree are hoping that their focus on tech, media and telecom — as well as some untraditional features, including a publicly traded investment vehicle, a weekly newsletter and podcast — will lead to success.

Since founding LionTree in 2012 with a fellow UBS alumnus, Ehren Stenzler, Mr. Bourkoff has steadily expanded the firm’s reach, opening offices in San Francisco, London and Paris. And he has begun to poach brand-name talent: Last year, LionTree hired Jake Donavan, who led European industry coverage for JPMorgan Chase’s investment bank, as president of its European division.

“The pitch was, ‘help me build something fun and exciting,’” Mr. Donavan said in an interview. Referring to how Wall Street refers to tech, media and telecom, he added, “It’s a unique time in the T.M.T. ecosystem.”

LionTree remains a relative minnow in the world of deal making. The 60-person firm has cracked the top 25 advisers on worldwide tech, media and telecom takeovers three times since its founding, according to Thomson Reuters. Its advisory business’s best year to date was in 2015, when it ranked eighth, outpacing every other independent bank. Last year, it ranked 24th, behind firms like Evercore and Raine Group. (LionTree did not have a role in the Disney deal, even though other boutique banks were involved.)

But the company, whose offices reflect a sort of sleekly modernized “Mad Men” décor, match Mr. Bourkoff’s vision for what his bank should look like.

Few in the firm have formal titles, in what is meant to create a “flat” organization in which young bankers can feel free to propose transaction ideas. Much effort has been spent on data analysis and reaching out to young tech start-ups run by millennial founders.

LionTree has worked to grow its investment management business, which uses outside client money to invest in transactions, often alongside advisory clients. This year, the firm backed a new investment company, Ocelot, that will use the $425 million that it raised from public-market investors, including Mr. Malone, to buy a privately held business.

And Mr. Bourkoff has also hired a number of advisers to serve as “entrepreneurs in residence,” including Ursula Burns, the former chief executive of Xerox, and Betsy Morgan, the former chief executive of Glenn Beck’s The Blaze, who are meant to both bring in business opportunities and come up with new initiatives. (It was Ms. Morgan, for instance, who helped come up with the idea of the firm’s KindredCast podcast, which has featured the likes of Mr. Moonves of CBS and the talent manager Scooter Braun.)

Yet at the center of LionTree remains Mr. Bourkoff. Mr. Malone — who controls the Liberty constellation of companies — called him the “honeybee” of the T.M.T. world, flying from flower to flower cross-pollinating ideas.

Mr. Bourkoff began his career as an analyst, first covering the debt of companies, and then their stocks. He then made the leap into investment banking at UBS, where he eventually became the Swiss bank’s head of investment banking for the Americas. He resigned in 2012 to co-found LionTree.

“The streets are littered with research analysts who tried to make the transition to investment banking, who thought they could leverage their relationships,” Rob Wiesenthal, once the chief financial officer of Sony Music and now the chief of Blade, the helicopter-ride start-up, said. “Aryeh is one of the only ones who has successfully done that.”

Ken Lerer, a co-founder of HuffPost and now a Viacom board member, credited Mr. Bourkoff with helping to resolve an impasse over the makeup of Viacom’s board involving Shari Redstone, the daughter of its chairman.

“It was a deal that wasn’t getting done otherwise,” Mr. Lerer said.

Among LionTree’s most prized clients is Liberty and Mr. Malone, who have retained the firm on numerous assignments.

“When people ask me, ‘Who should I use,’ he’s sort of the top of my list as an adviser,” Mr. Malone said in an interview.

But changing the perception that LionTree centers solely around Mr. Bourkoff may be difficult. “This is the Aryeh show,” Mr. Wiesenthal said. “This is not the LionTree show.”

Mr. Bourkoff is working to alter that view. He argued that his Rolodex belongs to the firm, because he cannot meet every client, come up with every idea and execute every deal. “It’s less important to have a branded banker than it is to have a system,” he said.

Young bankers are encouraged to pass along their business ideas to senior executives and to speak more to clients like Mr. Lerer and Charter’s management team. It is, in Mr. Bourkoff’s view, an extension of the networking that he himself practices constantly.

The challenge now is to grow the firm while not losing sight of what is happening in the tech, media and telecom worlds now, according to Mr. Bourkoff.

“We expect a frenetic year ahead,” he wrote in a letter to clients this weekend.

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